Advertisement

Analytical study of superradiant instability of the five-dimensional Kerr–Gödel black hole

Regular Article - Theoretical Physics

Abstract

We present an analytical study of the superradiant instability of the rotating asymptotically Gödel black hole (Kerr–Gödel black hole) in five-dimensional minimal supergravity theory. By employing the matched asymptotic expansion method to solve the Klein–Gordon equation of a scalar field perturbation, we show that the complex parts of quasinormal frequencies are positive in the regime of superradiance. This implies a growing instability of superradiant modes. The reason for this kind of instability is the Dirichlet boundary condition at asymptotic infinity, which is similar to that of rotating black holes in anti-de Sitter (AdS) spacetime.

Keywords

Black Hole Event Horizon Dirichlet Boundary Condition Quasinormal Mode Massless Scalar Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author would like to thank Ming-Fan Li for reading the manuscript and useful comments. This work was supported by NSFC, China (Grant No. 11147145 and No. 11205048).

References

  1. 1.
    Ya.B. Zel’dovich, Pis’ma Zh. Eksp. Teor. Fiz. 14, 270 (1971). [JETP Lett. 14, 180 (1971)] Google Scholar
  2. 2.
    Ya.B. Zel’dovich, Zh. Eksp. Teor. Fiz. 62, 2076 (1972). [Sov. Phys. JETP 35, 1085 (1972)] Google Scholar
  3. 3.
    J.M. Bardeen, W.H. Press, S.A. Teukolsky, Astrophys. J. 178, 347 (1972) ADSCrossRefGoogle Scholar
  4. 4.
    C.W. Misner, Bull. Am. Phys. Soc. 17, 472 (1972) Google Scholar
  5. 5.
    A.A. Starobinsky, Zh. Eksp. Teor. Fiz. 64, 48 (1973). [Sov. Phys. JETP 37, 28 (1973)] ADSGoogle Scholar
  6. 6.
    A.A. Starobinsky, S.M. Churilov, Zh. Eksp. Teor. Fiz. 65, 3 (1973). [Sov. Phys. JETP 38, 1 (1973)] ADSGoogle Scholar
  7. 7.
    W.H. Press, S.A. Teukolsky, Nature (London) 238, 211 (1972) ADSCrossRefGoogle Scholar
  8. 8.
    V. Cardoso, O.J.C. Dias, J.P.S. Lemos, S. Yoshida, Phys. Rev. D 70, 044039 (2004) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    S. Hod, O. Hod, Phys. Rev. D 81, 061502 (2010) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    J.G. Rosa, J. High Energy Phys. 1006, 015 (2010) MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    J.-P. Lee, Mod. Phys. Lett. A 27, 1250038 (2012) ADSCrossRefGoogle Scholar
  12. 12.
    T. Damour, N. Deruelle, R. Ruffini, Lett. Nuovo Cimento Soc. Ital. Fis. 15, 257 (1976) ADSCrossRefGoogle Scholar
  13. 13.
    S. Detweiler, Phys. Rev. D 22, 2323 (1980) ADSCrossRefGoogle Scholar
  14. 14.
    T.M. Zouros, D.M. Eardley, Ann. Phys. (N.Y.) 118, 139 (1979) ADSCrossRefGoogle Scholar
  15. 15.
    H. Furuhashi, Y. Nambu, Prog. Theor. Phys. 112, 983 (2004) ADSzbMATHCrossRefGoogle Scholar
  16. 16.
    M.J. Strafuss, G. Khanna, Phys. Rev. D 71, 024034 (2005) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    S.R. Dolan, Phys. Rev. D 76, 084001 (2007) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    S. Hod, Phys. Lett. B 708, 320 (2012) ADSCrossRefGoogle Scholar
  19. 19.
    R.A. Konoplya, Phys. Lett. B 666, 283 (2008) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    O.J.C. Dias, Phys. Rev. D 73, 124035 (2006) ADSCrossRefGoogle Scholar
  21. 21.
    V. Cardoso, O.J.C. Dias, Phys. Rev. D 70, 084011 (2004) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    V. Cardoso, O.J.C. Dias, S. Yoshida, Phys. Rev. D 74, 044008 (2006) ADSCrossRefGoogle Scholar
  23. 23.
    A.N. Aliev, O. Delice, Phys. Rev. D 79, 024013 (2009) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    N. Uchikata, S. Yoshida, Phys. Rev. D 83, 064020 (2011) ADSCrossRefGoogle Scholar
  25. 25.
    R. Li, Phys. Lett. B 714, 337 (2012) MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    G. Clement, D. Galtsov, C. Leygnac, Phys. Rev. D 67, 024012 (2003) MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    R.A. Konoplya, A. Zhidenko, Phys. Rev. D 84, 104022 (2011) ADSCrossRefGoogle Scholar
  28. 28.
    E.G. Gimon, A. Hashimoto, Phys. Rev. Lett. 91, 021601 (2003) MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    K. Gödel, Rev. Mod. Phys. 21, 447 (1949) ADSzbMATHCrossRefGoogle Scholar
  30. 30.
    G. Barnich, G. Compere, Phys. Rev. Lett. 95, 031302 (2005) MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    S.Q. Wu, J.J. Peng, Phys. Rev. D 83, 044028 (2011) ADSCrossRefGoogle Scholar
  32. 32.
    R.A. Konoplya, E. Abdalla, Phys. Rev. D 71, 084015 (2005) MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    S.B. Chen, B. Wang, J.L. Jing, Phys. Rev. D 78, 064030 (2008) MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    X. He, B. Wang, S.B. Chen, Phys. Rev. D 79, 084005 (2009) MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    W. Li, L. Xu, M. Liu, Class. Quantum Gravity 26, 055008 (2009) MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    S.Q. Wu, Phys. Rev. Lett. 100, 121301 (2008) ADSCrossRefGoogle Scholar
  37. 37.
    R.A. Konoplya, A. Zhidenko, Phys. Rev. D 84, 064028 (2011) ADSCrossRefGoogle Scholar
  38. 38.
    W.A. Hiscock, Phys. Rev. D 17, 1497 (1978) MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    S.N. Guha Thakurta, Phys. Rev. D 21, 864 (1980) MathSciNetADSCrossRefGoogle Scholar
  40. 40.
    R.A. Konoplya, Phys. Lett. B 706, 451 (2012) ADSCrossRefGoogle Scholar
  41. 41.
    R.A. Konoplya, A. Zhidenko, arXiv:1110.2015 [hep-th]
  42. 42.
    H. Kodama, Prog. Theor. Phys. Suppl. 172, 11 (2008). arXiv:0711.4184 [hep-th] ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Department of PhysicsHenan Normal UniversityXinxiangChina

Personalised recommendations